# Dimensionality Reduction and Dynamical Mode Recognition of Circular Arrays of Flame Oscillators Using Deep Neural Network

arXiv: https://arxiv.org/abs/2312.02462 · HTML: https://mlsanity.com/paper/2312.02462/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 96 references that are in the map.
- First posted on arXiv 5 Dec 2023.

## Builds on (most cited first, 11 of 11)

- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Quantization and Training of Neural Networks for Efficient Integer-Arithmetic-Only Inference](https://mlsanity.com/paper/1712.05877/) (2017)
- [Temporal Convolutional Networks for Action Segmentation and Detection](https://mlsanity.com/paper/1611.05267/) (2016)
- [Tutorial on Variational Autoencoders](https://mlsanity.com/paper/1606.05908/) (2016)
- [Statistical Aspects of Wasserstein Distances](https://mlsanity.com/paper/1806.05500/) (2018)
- [β-Variational autoencoders and transformers for reduced-order modelling of fluid flows](https://mlsanity.com/paper/2304.03571/) (2023)
- [Sig-Wasserstein GANs for Time Series Generation](https://mlsanity.com/paper/2111.01207/) (2021)
- [Learning physics-based reduced-order models for a single-injector combustion process](https://mlsanity.com/paper/1908.03620/) (2019)
- [Dynamical Wasserstein Barycenters for Time-series Modeling](https://mlsanity.com/paper/2110.06741/) (2021)
- [Latent Variable Models in the Era of Industrial Big Data: Extension and Beyond](https://mlsanity.com/paper/2208.10847/) (2022)
- [Nonparametric and Regularized Dynamical Wasserstein Barycenters for Sequential Observations](https://mlsanity.com/paper/2210.01918/) (2022)

## Built on by (most cited first, 1 of 1)

- [Stabilization Analysis and Mode Recognition of Kerosene Supersonic Combustion: A Deep Learning Approach Based on Res-CNN-beta-VAE](https://mlsanity.com/paper/2503.12765/) (2025)

## Abstract (arXiv)

Oscillatory combustion in aero engines and modern gas turbines often has significant adverse effects on their operation, and accurately recognizing various oscillation modes is the prerequisite for understanding and controlling combustion instability. However, the high-dimensional spatial-temporal data of a complex combustion system typically poses considerable challenges to the dynamical mode recognition. Based on a two-layer bidirectional long short-term memory variational autoencoder (Bi-LSTM-VAE) dimensionality reduction model and a two-dimensional Wasserstein distance-based classifier (WDC), this study proposes a promising method (Bi-LSTM-VAE-WDC) for recognizing dynamical modes in oscillatory combustion systems. Specifically, the Bi-LSTM-VAE dimension reduction model was introduced to reduce the high-dimensional spatial-temporal data of the combustion system to a low-dimensional phase space; Gaussian kernel density estimates (GKDE) were computed based on the distribution of phase points in a grid; two-dimensional WD values were calculated from the GKDE maps to recognize the oscillation modes. The time-series data used in this study were obtained from numerical simulations of circular arrays of laminar flame oscillators. The results show that the novel Bi-LSTM-VAE method can produce a non-overlapping distribution of phase points, indicating an effective unsupervised mode recognition and classification. Furthermore, the present method exhibits a more prominent performance than VAE and PCA (principal component analysis) for distinguishing dynamical modes in complex flame systems, implying its potential in studying turbulent combustion.